Nicotine withdrawal is condition where someone addicted to nicotine (like from smoking Cigarettes) does not receive their regular dose. Symptoms from the withdrawal include anger and depression, but it is not life-threatening. Eventually, the nicotine could breakdown and one would no longer feel the effects.
Since Dr. Nicholas Rush was a smoker, he began suffering from the effects of the withdrawal during the first few days aboard Destiny as there wasn't any source of nicotine aboard. Since he also drank several cups of coffee a day, this was accompanied by caffeine withdrawal. Lt. Tamara Johansen reported that others on board also showed signs of withdrawal. (SGU: "Darkness")